Periodic surface for large scan angles

ABSTRACT

The invention is for a tuned resonant surface utilizing an array of short, loaded dipoles to obtain unity reflection or transmission coefficient over a narrow bandwidth about the desired frequency with said coefficient substantially independent of the angle of incidence of the impinging or radiated electromagnetic signal. Reference is made to the claims for a legal definition of the invention.

United States Patent 1191 Munk [ 1*Jan. 29, 1974 PERIODIC SURFACE FOR LARGE SCAN ANGLES [75] Inventor: Benedikt A. Munk, Columbus, Ohio [73] Assignee: The Ohio State University Research Foundation, Columbus, Ohio Notice: The portion of the term of this patent subsequent to Aug. 29, 1989, has been disclaimed.

[22] Filed: Oct. 16, 1968 [21] Appl. No.: 768,142

3,381,293 4/1968 Tarp1ey,.1r. ..343/1s13 OTHER PUBLICATIONS Wiekhorst, Absorption and Transmission of Electromagnetic Waves, 7, 1957 pp. 1-4, 23.

Luis L. Oh et al., Slotted Metal Radome Cap For Rain, Hail, and Lightning Protection, Microwave Journal, Mar. 1968 pp. 105-108.

Primary Examiner-T. H. Tubbesing Attorney, Agent, or Firm-Anthony D. Cennamo 5 7] ABSTRACT The invention is for a tuned resonant surface utilizing an array of short, loaded dipoles to obtain unity reflection or transmission coefficient over a narrow bandwidth about the desired frequency with said coefficient substantially independent of the angle of incidence of the impinging or radiated electromagnetic signal. Reference is made to the claims for a legal definition of the invention.

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ATTORNEY BACKGROUND A tuned resonant surface is a surface with a reflection or transmission coefficient which has resonance characteristics. In the prior art such a surface has been constructed of an array of resonant strips approximately M2 in length (resonant reflector) or an array of M2 in length slots (resonant window). With proper spacing unity reflection or transmission coefficients have been achieved at the resonant frequency. The resonant frequency of such an array is strongly dependent on the resonant frequency of the scattering elements and the bandwidth is dependent on both the bandwidth ofthe elements and the spacing between them. The resonant frequency is also dependent on the angle of incidence and the spacing between elements. The latter dependency is the result of the mutual impedances between the M2 strips (or slots). With a change in the angle of incidence there is a considerable frequency shift in the resonant frequency of the array. These arrays, therefore, have an undesirably wide bandwidth for some applications.

A radome constructed utilizing the M2 elements is severly limited in the maximum efficient scan angle possible and the boresight error is substantial.

SUMMARY OF THE INVENTION The invention relates to a tuned resonant surface comprising an array of resonant strips or slots. The configuration of said elements is that of a short M2) dipole loaded by a shorted two-wire transmission line. Due to the fact that the mutual impedance decreases greatly for short elements there is consequently a smaller-frequency shift of the resonant frequency of the array as a function of angle of incidence. The shorted two-wire transmission line is essential to the configuration to supply the inductive load necessary in order to obtain resonance for such a short element.

When functioning as a resonant reflector the surface comprises a dielectric substrate on which is constructed an array of elements formed from conductive material shaped in the configuration of the invention disclosed herein. When functioning as a resonant window the surface comprises a surface of electrically conductive material from which has been removed slots of the material in the configuration of the invention disclosed herein.

The present invention solves several problems previously existent in the prior art. With the proper design the resonant frequency of the surfaces of the invention are nearly independent of the angle of incidence when the incident angle is less than 65. This is a very important result which now makes it practical to use the tuned resonant surface, either as a reflector or as a window in the form ofa Babinet equivalent, in applications where the angle of incidence changes.

The bandwidth of this type of tuned resonant surface is significantly less than the smallest bandwidth yet obtained for a tuned resonant surface made of an array of resonant A /2 dipole elements. For one design considered in detail a reduction of nearly a factor of three in bandwidth is obtained, and even narrower bandwidths can be achieved with proper design.

The improvement obtained by the tuned resonant surface of the invention is due to the impedance properties of the short, loaded dipole element. The self impedance of the short dipole element is much greater than the mutual impedance and consequently the effects of coupling between scattering elements is reduced, thus significantly reducing the dependence on the angle of incidence. The narrow-band properties occur because the impedance of the short dipole element varies rapidly with frequency. An important practical application of such a surface would be the production of a radome for wide scanning purposes and minimum boresight error.

OBJECTS Accordingly, it is a principal object of the invention to provide an improved tuned resonant surface.

Another object of the invention is to provide a tuned resonant surface which provides a narrow bandwidth.

Another object of the invention is to provide a tuned resonant surface which provides a :reduced dependence of the resonant frequency on the incidence angle of the impinging radiation.

A further object ofthe invention is to provide a tuned resonant surface which permits the utilization of a wide scan angle.

Still a further object of the invention is to provide a tuned resonant surface which by proper design permits operation about a resonant frequency chosen from the entire scope of available frequencies.

For a complete understanding of the invention, together with other objects and advantages thereof, reference may be made to the accompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1a is a graphical representation of the reflection coefficient (dB below equilvalent plate) of a state-ofthe-art M2 dipole array as a function of frequency;

FIG. lb illustrates the physical dimensions of the state-of-the-art M2 dipole array used to obtain the graph of FIG. 1a;

FIG. 2a represents a preferred embodiment of an element of the invention;

FIG. 2b is a schematic representation ofthe preferred embodiment of the invention comprising an array of the short, loaded dipoles shown in FIG. 2a;

FIGS. 26 and 2d represent alternative embodiments of an element of the invention utilizing a coil for tuning;

FIG. 2e represents an alternative embodiment of an element of the invention utilizing a piece of ferrite for tuning;

FIG. 2f represents an alternative embodiment of an element of the invention in which two of the elements shown in FIG. 2a are attached together;

FIG. 3 is a graphical representation of the impedance characteristics of the preferred embodiment of the invention illustrated in FIG. 2b;

FIG. 4a, 4b, and 4c are graphical representations of the calculated detuning of the resonance frequency for an array of short, loaded dipoles of the preferred embodiment, as illustrated in FIG. 2b, for a constant ratio of the interelement spacing in the H-plane, D, to the wavelength, A, as a function of the angle of incidence. The ratio (D/X), is equal to 0.40, 0.60, and 0.65 in FIGS. 4a, 4b, and 4c, respectively. Also shown in FIG. 411, for comparison purposes, is the same curve for M2 dipoles in half scale;

FIG. 5 is a graphical representation of the effect of the slope of X for the preferred embodiment illustrated in FIG. 2b on the value of A (UK);

FIG. 6a is a graphical representation of the reflection coefficient (dB below equivalent plate) of an array of the preferred embodiment elements illustrated in FIG. 2b as a function of frequency;

FIG. 6b illustrates the physical dimensions of the preferred embodiment array used to obtain the graph of FIGf6a;

FIG. 7 represents an alternative embodiment of the invention wherein two panels of tuned resonant surfaces are stacked; and,

FIG. 8 is a graphical representation of the reflection coefficient (dB below equivalent plate) as a function of frequency for various angles of incidence computed from the alternative embodiment illustrated in FIG. 7.

DETAILED DESCRIPTION OF THE DRAWINGS Referring now to FIG. Ia there is represented a graph of the reflection response as a function of frequency obtained from a tuned resonant surface. This tuned resonant surface was constructed with the elements shown in FIG. lb. This construction is representative of that of the prior art. It consists of conducting plates arranged in an array. These conducting plates or elements are approximately M2 (A wavelength) in length. With this construction the tuned resonant surface would be a reflector at the resonant frequency. By utilizing this configuration and all the other configurations discussedin this specification as a slot in a conducting medium rather than as a conducting element in a dielectric medium the tuned resonant surfaces will represent a window to the impinging signals. The surface will, therefore, transmit rather than reflect those signals at the resonant frequency for which the surface is tuned. For purposes of this disclosure only, the reflective mode will be discussed.

The resonant frequency for which the length of the individual elements is chosen will determine in part the resonant frequency of the array. The bandwidth of the array is dependent upon the bandwidth of the elements and the spacing between them. The resonant frequency of the total array is also dependent on the angle of incidence 6 of the impinging electromagnetic radiation and the spacing between the elements.

As illustrated in FIG. la the bandwidth of the surface is very broad about the chosen resonant frequency. The mutual impedance between the individual elements is substantial and is the factor which causes the frequency response of'the array of FIG. lb to be very dependent upon the angle of incidence, 0.

FIG. 2a shows the configuration of an element designed in conformance with the teachings of the present invention. FIG. 2b is a schematic representation of the preferred embodiment of the invention comprising an array of the short, loaded dipoles shown iqn FIG. 2a. The element shown in FIG. 2a comprises two short elements, 2 and 4, of conducting material. By short, it is meant an element less than M2 in length. These elements are formed in the shape of a dipole and the dipole is loaded with and tuned by a two-wire transmission line 6 which is electrically shorted at the far end. As shown in FIG. 2b it is not essential to the operation of the invention that the elements have an upward turn on the ends of the dipole segments.

The purpose of the transmission line 6 is to tune the short dipole to maximum radar cross section at a predetermined resonant frequency. The tuning is accomplished by the matching of the capacitance of the dipole with an inductive load. This cancellation of impedances will cause resonance in the element at the desired frequency. Therefore, with a given capacitance (i.e., given dipole) the addition of an inductive load will cause a resultant drop in the resonance frequency of the element.

The tuning function performed by the shorted transmission line could be accomplished by the use of an inductive element, such as, for example, a coil (see FIGS. 20 and 2d) or a piece of ferrite (see FIG. 2e). This application is, therefore, not to be limited to tuning by shorted transmission line.

By proper design the predetermined resonant frequency can be any frequency desired within size limitations. The mutual impedance of the elements in the array decreases greatly for short elements and thereby results a smaller frequency shift from the chosen frequency as a function of the angle of incidence.

FIG. 2f illustrates an alternative embodiment of the invention in which two of the elements shown in FIG. 2a are positioned so that the surface will reflect two polarizations. This is accomplished by the element's symmetrical dipole and shorted transmission line portions reversing roles when the impinging radiation is switched from horizontal to vertical polarization.

The following shows the derivation of an expression for the resonant frequency,f,,.,,, ofa tuned resonant surface array as illustrated in FIG. 2b. The effect of all dipoles is to produce in the reference dipole an apparent 1 change of its impedance equal to the mutual impedance given by Zm=AZ=2 2g 0,. cos (BkD sin 0), V r =1 where Z mutual impedance between the reference element and the element and on the k'" column and the r"' row,

0 the angle of incidence in the H-plane, and

D interelement spacing in the H-plane, and

A shift in the imaginary part (A X) of Z,, will produce a shift in the resonant frequency of the scattered field as predicted by the intersection of the load reactance (X curve and the antenna reactance (X,,) curve (see FIG. 3). It is also seen in FIG. 3 that the slope of X,, is very much less than the slope of X,., or X and consequently X,,, is assumed to be constant. In this case, the resonant frequency occurs for an element length l/)\ A l/ as shown in FIG. 3, where where AX is measured in ohms. Finally 7P8)/ r(s Substituting Eq. (2) into Eq. (3) yields Af/f 100 percent 0.133 AX.

This value is for the particular design under consideration.

The calculated Af/f as a function of angle of incidence according to Eq. (4) is shown in FIGS. 4a, 4b, and 40, for D/)\ 0.40, 0.60, and 0.65, respectively. It is interesting to compare these curves with those shown in FIG. 1a corresponding to the frequency shift for M2 strips with the same spacing (shown in one case in FIG. 412 for comparison). It is observed that the antiresonance occurs at the same value of for the two types of elements but that the magnitude of the resonant shift is greatly reduced as the angle of incidence is changed for the short, loaded elements. There are two principal reasons for this effect. First, the magnitude of the mutual impedance is reduced approximately by the ratio between the square of the element lengths. Second, the summation of the mutual impedance given by Eq. (1) is a function of the angle of incidence, 0. Altering the angle of incidence produces a change in A (l/h) given by Eq. (2). Since the sign of the mutual impedance or the component AX is, for 0=0, the same as illustrated in FIG. 3 and in FIG. 4b, the slope of the load reactance X acts to reduce A (l/)\) as compared to A (l/)\)' (as shown in FIG. 5). A much smaller contributing factor is seen to be the slightly higher slope of X at (l/ 0.15 than at (I/)\) z 0.25.

A complete measured resonant curve for a tuned resonant surface constructed with the short, loaded dipoles of the invention is shown graphically in FIG. 6a as a function of the angle of incidence. The interelement spacing was 0.35 inches in the horizontal and 0.70 inches in the vertical directions as shown in FIG. 6b. This corresponds, for the resonant frequency 1 1.2 GHz, to D/)\ =0.35. The calculated values of Af taken from a graph similar to those illustrated in FIG. 4 agreed within 1 percent or better with the measured values. (Note this is merely a calculation of the frequency shift related to the resonance frequency, 1 1.2 GHz.)

It is further seen from FIG. 60 that the peak value is somewhat low; i.e., approximately 0.2 dB below the equivalent plate as determined by the backscattered patterns. This is the result of the loss tangent of the dielectric backing on which the conducting elements are constructed and also by the finiteness of the small array used for test measurement purposes. This dB loss could be substantially reduced by the correct choice of dielectric backing material for each design. The presence of the dielectric substrate is not essential to the operation of the invention. It would be desirable to completely eliminate the substrate. A substrate was used in the construction of the experimental models because it provided a convenient structure on which the elements could be photoetched.

There is illustrated in FIG. 7 an alternative embodiment of the invention. FIG. 8 shows in graphical form a characteristic curve of the embodiment of FIG. 7. The power coefficient is plotted as a function of frequency for various angles of incidence. It can be seen from FIG. 8 that there is a substantial decrease in the bandwidth of the array about the resonant frequency. The curves have a flat top and rapidly falling sides. This permits operation in a narrow band of frequencies with essentially unity reflection (or transmission, depending on whether conducting elements or slots are utilized). The values used to plot FIG. 8 were calculated but measurements of the same function have given results which compare excellently with the calculated values. The stacking of the arrays, therefore, permits a close approximation to squarewave waveshape which is the ideal waveshape for tuned resonant structures. The ideal waveshape is more closely approximated as the number of layers of tuned resonant surfaces is increased. As the number oflayers is increased the selectivity is increased.

The construction of a multilayer structure is also within the teaching of this specification. A multilayer structure comprises elements tuned for different frequencies. This is accomplished by utilizing elements tuned to different frequencies on the same tuned resonant surface or by the stacking of surfaces with each surface possessing elements tuned to the same resonant frequency but different resonant frequencies among the individual surfaces.

Although certain and specific embodiments have been illustrated, it is to be understood that modifications may be made without departing from the true spirit and scope of the invention.

What is claimed is:

l. A tuned resonant surface antenna having a unity reflection or transmission coefficient over a narrow bandwith about the desired frequency comprising an array of resonant short dipole elements of less than one-half the wavelength (M2) in length loaded by a two-wire transmission line, said coefficient being substantially independent of the angle of incidence of the. electromagnetic signal, and wherein the resonant frequency of said surface is dependant in the length of said elements and the spacing between. said elements.

2. A tuned resonant surface as set forth in claim 1 wherein said array of resonant elements comprises a plurality of electrically conductive tuned resonant strips.

3. A tuned resonant surface as set forth in claim 2 wherein said array of resonant elements is formed upon a dielectric substrate.

4. A tuned resonant surface as set forth in claim 1 comprising means to tune said array of dipoles to a predetermined resonant frequency including an inductive load, means connecting the two elements of each of said dipoles to said load to provide an inductance to match the capacitance of said dipoles at said resonant frequency.

5. A tuned resonant surface as set forth in claim 4 wherein said means to tune said array to a predetermined resonant frequency comprises a shorted twowire transmission line.

6. A tuned resonant surface as :set forth in claim 4 wherein said means to tune said array to a predetermined resonant frequency comprises a coil.

7. A tuned resonant surface as set forth in claim 4 wherein said means to tune said array to a predetermined resonant frequency comprises a piece of ferrite.

8. A tuned resonant surface comprising an array of resonant elements, said elements comprising two strips of electrically conductive material positioned in a straight line in the form of a dipole of less than one-half the wavelength (M2) in length; a pair of parallel electrically conductive strips, the first of said parallel strips electrically attached to one of the internal ends of said dipole and the second of said parallel strips electrically attached to the other of the internal ends of said dipole; a third strip of electrically conductive material joining the ends of said parallel conducting strips at the ends remote from said dipole.

9. A multilayer tuned resonant structure comprising a plurality of tuned resonant surfaces stacked one above the other, each of said surfaces comprising an array of resonant short dipoles of less than one-half the wavelength (M2) in length.

said gammadion a closed figure. 

1. A tuned resonant surface antenna having a unity reflection or transmission coefficient over a narrow bandwith about the desired frequency comprising an array of resonant short dipole elements of less than one-half the wavelength ( lambda /2) in length loaded by a two-wire transmission line, said coefficient being substantially independent of the angle of incidence of the electromagnetic signal, and wherein the resonant frequency of said surface is dependant in the length of said elements and the spacing between said elements.
 2. A tuned resonant surface as set forth in claim 1 wherein said array of resonant elements comprises a plurality of electrically conductive tuned resonant strips.
 3. A tuned resonant surface as set forth in claim 2 wherein said array of resonant elements is formed upon a dielectric substrate.
 4. A tuned resonant surface as set forth in claim 1 comprising means to tune said array of dipoles to a predetermined resonant frequency including an inductive load, means connecting the two elements of each of said dipoles to said load to provide an inductance to match the capacitance of said dipoles at said resonant frequency.
 5. A tuned resonant surface as set forth in claim 4 wherein said means to tune said array to a predetermined resonant frequency comprises a shorted two-wire transmission line.
 6. A tuned resonant surface as set forth in claim 4 wherein said means to tune said array to a predetermined resonant frequency comprises a coil.
 7. A tuned resonant surface as set forth in claim 4 wherein said means to tune said array to a predetermined resonant frequency comprises a piece of ferrite.
 8. A tuned resonant surface comprising an array of resonant elements, said elements comprising two strips of electrically conductive material positioned in a straight line in the form of a dipole of less than one-half the wavelength ( lambda /2) in length; a pair of parallel electrically conductive strips, the first of said parallel strips electrically attached to one of the internal ends of said dipole and the second of said parallel strips electrically attached to the other of the internal ends of said dipole; a third strip of electrically conductive material joining the ends of said parallel conducting strips at the ends remote from said dipole.
 9. A multilayer tuned resonant structure comprising a plurality of tuned resonant surfaces stacked one above the other, each of said surfaces comprising an array of resonant short dipoles of less than one-half the wavelength ( lambda /2) in length.
 10. A multilayer tuned resonant structure as set forth in claim 9 wherein all of said resonant surfaces are tuned for the same resonant frequency.
 11. A multilayer tuned resonant structure as set forth in claim 9 wherein each of said resonant surfaces is tuned for a different resonant frequency.
 12. A tuned resonant surface comprising an array of resonant elements, said elements comprising eight strips of electrically conductive material positioned in parallel pairs to form a gammadion and four strips of electrically conductive material joining the external ends of said parallel conducting strips, thereby making said gammadion a closed figure. 